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Let f(x)={(1+3x)^(1/x),x!=0e^3,x=0dotD i...

Let `f(x)={(1+3x)^(1/x),x!=0e^3,x=0dotD i s c u s st h econ t inu i t yof` `f(x)` at `(a)x=0,` (b) `x=1.`

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BANSAL-CONTINUITY AND DIFFERENTIABILITY-All Questions
  1. Sketch the graph of the following function f(x)=|ln|x||

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  2. The function f:""R""~""{0}vecR given by f(x)=1/x-2/(e^(2x)-1) ca...

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  3. Let f(x)={(1+3x)^(1/x),x!=0e^3,x=0dotD i s c u s st h econ t inu i t y...

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  4. Which of the following functions is not continuous AAx in R ? sqrt(2...

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  5. Discuss the continuity of f(x)={(x^4-5x^2+4)/(|(x-1)(x-2)|),x!=1,2, 6...

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  7. lim(x->0)f(x)=(x^3-x)/(x^2-1)

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  8. What is the range of the function f(x)=[|x-1|]/[x-1]

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  9. f(x)={|x+1|;xlt=0x ;x >0 and g(x)={|x|+1;xlt=1-|x-2|;x >1 Draw its g...

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  10. Show that the function f(x)=(x-a)^2(x-b)^2+x takes the value (a+b)/2 f...

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  11. Suppose that f(x) is continuous in [0, 1] and f(0) = 0, f(1) = 0. Prov...

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  12. Let f be a continuous function defined onto [0,1] with range [0,1]. Sh...

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  13. Leg f be continuous on the interval [0,1] to R such that f(0)=f(1)dot ...

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  14. Let f:[0,1]vec[0,1] be a continuous function. Then prove that f(x)=x f...

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  15. Discuss the continuity of the function ([.] represents the greatest ...

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  16. Discuss the continuity of the function ([.] represents the greatest ...

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  17. Discuss the continuity of the function ([.] represents the greatest ...

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  18. Draw the graph and find the points of discontinuity f(x) = [2cos x] , ...

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  19. If the function f(x)=[((x-2)^3)/a]sin(x-2)+acos(x-2),[dot] denotes the...

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  20. Discuss the continuity of f(x)=sgn(x^3-x)

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